A robust mixed functional classifier with adaptive large margin loss

Functional classification has been increasingly helpful in exploring and predicting a response variable with multiple categories. In fact, both functional and scalar covariates may be useful and should be included in the model simultaneously, and thus developing a robust multi-categorical functional classifier with statistical guarantees is desirable. However, both of these two issues are rarely touched in previous studies. Motivated by these, in this paper we propose a novel large margin linear mixed functional classifier for the response with multiple categories, which includes both functional and scalar covariates as predictors, especially when functional data are sparsely longitudinal. Not only does the proposed method address the functional classification using a combination of both functional and scalar covariates, but also provides a robust multi-categorical mixed functional classifier using a large margin loss adaptive to observed samples. Furthermore, we establish statistical theories of a mixed functional classifier, which have been less considered in existing literature. An efficient algorithm is also proposed for its practical implementation. Numerical investigations have supported the superb performance of the proposed method on both simulated and real datasets.